Fundamentals of three-dimensional reconstruction from projections

Seeing the Supracolloidal Assemblies in 3D: Unraveling High-Resolution Structures Using Electron Tomography

Transmission electron microscopy (TEM) imaging has revolutionized modern materials science, nanotechnology, and structural biology. Its ability to provide information about materials' structure, composition, and properties at atomic-level resolution has enabled groundbreaking discoveries and the development of innovative materials with precision and accuracy. Electron tomography, single particle reconstruction, and microcrystal electron diffraction techniques have paved the way for the three-dimensional (3D) reconstruction of biological samples, synthetic materials, and hybrid nanostructures at near atomic-level resolution. TEM tomography using a series of two-dimensional (2D) projections has been used extensively in biological science, but in recent years it has become an important method in synthetic nanomaterials and soft matter research. TEM tomography offers unprecedented morphological details of 3D objects, internal structures, packing patterns, growth mechanisms, and self-assembly pathways of self-assembled colloidal systems. It complements other analytical tools, including small-angle X-ray scattering, and provides valuable data for computational simulations for predictive design and reverse engineering of nanomaterials with the desired structure and properties. In this perspective, I will discuss the importance of TEM tomography in the structural understanding and engineering of self-assembled nanostructures with specific emphasis on colloidal capsids, composite cages, biohybrid superlattices with complex geometries, polymer assemblies, and self-assembled protein-based superstructures.

Structural Analysis of Protein Complexes by Cryo-Electron Microscopy

Structural studies of bio-complexes using single particle cryo-Electron Microscopy (cryo-EM) is nowadays a well-established technique in structural biology and has become competitive with X-ray crystallography. Development of digital registration systems for electron microscopy images and algorithms for the fast and efficient processing of the recorded images and their following analysis has facilitated the determination of structures at near-atomic resolution. The latest advances in EM have enabled the determination of protein complex structures at 1.4-3 Å resolution for an extremely broad range of sizes (from ~100 kDa up to hundreds of MDa (Bartesaghi et al., Science 348(6239):1147-1151, 2015; Herzik et al., Nat Commun 10:1032, 2019; Wu et al., J Struct Biol X 4:100020, 2020; Zhang et al., Nat Commun 10:5511, 2019; Zhang et al., Cell Res 30(12):1136-1139, 2020; Yip et al., Nature 587(7832):157-161, 2020; https://www.ebi.ac.uk/emdb/statistics/emdb_resolution_year )). In 2022, nearly 1200 structures deposited to the EMDB database were at a resolution of better than 3 Å ( https://www.ebi.ac.uk/emdb/statistics/emdb_resolution_year ).To date, the highest resolutions have been achieved for apoferritin, which comprises a homo-oligomer of high point group symmetry (O432) and has rigid organization together with high stability (Zhang et al., Cell Res 30(12):1136-1139, 2020; Yip et al., Nature 587(7832):157-161, 2020). It has been used as a test object for the assessments of modern cryo-microscopes and processing methods during the last 5 years. In contrast to apoferritin bacterial secretion systems are typical examples of multi protein complexes exhibiting high flexibility owing to their functions relating to the transportation of small molecules, proteins, and DNA into the extracellular space or target cells. This makes their structural characterization extremely challenging (Barlow, Methods Mol Biol 532:397-411, 2009; Costa et al., Nat Rev Microbiol 13:343-359, 2015). The most feasible approach to reveal their spatial organization and functional modification is cryo-electron microscopy (EM). During the last decade, structural cryo-EM has become broadly used for the analysis of the bio-complexes that comprise multiple components and are not amenable to crystallization (Lyumkis, J Biol Chem 294:5181-5197, 2019; Orlova and Saibil, Methods Enzymol 482:321-341, 2010; Orlova and Saibil, Chem Rev 111(12):7710-7748, 2011).In this review, we will describe the basics of sample preparation for cryo-EM, the principles of digital data collection, and the logistics of image analysis focusing on the common steps required for reconstructions of both small and large biological complexes together with refinement of their structures to nearly atomic resolution. The workflow of processing will be illustrated by examples of EM analysis of Type IV Secretion System.

Evaluation of Electron Tomography Capabilities for Shale Imaging

Despite the advantageous resolution of electron tomography (ET), reconstruction of three-dimensional (3D) images from multiple two-dimensional (2D) projections presents several challenges, including small signal-to-noise ratios, and a limited projection range. This study evaluates the capabilities of ET for thin sections of shale, a complex nanoporous medium. A numerical phantom with 1.24 nm pixel size is constructed based on the tomographic reconstruction of a Barnett shale. A dataset of 2D projection images is numerically generated from the 3D phantom and studied over a range of conditions. First, common reconstruction techniques are used to reconstruct the shale structure. The reconstruction uncertainty is quantified by comparing overall values of storage and transport metrics, as well as the misclassification of pore voxels compared to the phantom. We then select the most robust reconstruction technique and we vary the acquisition conditions to quantify the effect of artifacts. We find a strong agreement for large pores over the different acquisition workflows, while a wider variability exists for nanometer-scale features. The limited projection range and reconstruction are identified as the main experimental bottlenecks, thereby suggesting that sample thinning, advanced holders, and advanced reconstruction algorithms offer opportunities for improvement.

Visualizing the membrane disruption action of antimicrobial peptides by cryo-electron tomography

The abuse of antibiotics has led to the emergence of multidrug-resistant microbial pathogens, presenting a pressing challenge in global healthcare. Membrane-disrupting antimicrobial peptides (AMPs) combat so-called superbugs via mechanisms different than conventional antibiotics and have good application prospects in medicine, agriculture, and the food industry. However, the mechanism-of-action of AMPs has not been fully characterized at the cellular level due to a lack of high-resolution imaging technologies that can capture cellular-membrane disruption events in the hydrated state. Previously, we reported PepD2M, a de novo-designed AMP with potent and wide-spectrum bactericidal and fungicidal activity. In this study, we use cryo-electron tomography (cryo-ET) and high-speed atomic force microscopy (HS-AFM) to directly visualize the pepD2M-induced disruption of the outer and inner membranes of the Gram-negative bacterium Escherichia coli, and compared with a well-known pore-forming peptide, melittin. Our high-resolution cryo-ET images reveal how pepD2M disrupts the E. coli membrane using a carpet/detergent-like mechanism. Our studies reveal the direct membrane-disrupting consequence of AMPs on the bacterial membrane by cryo-ET, and this information provides critical insights into the mechanisms of this class of antimicrobial agents.

Correlating cryo-super resolution radial fluctuations and dual-axis cryo-scanning transmission electron tomography to bridge the light-electron resolution gap

Visualization of organelles and their interactions with other features in the native cell remains a challenge in modern biology. We have introduced cryo-scanning transmission electron tomography (CSTET), which can access 3D volumes on the scale of 1 micron with a resolution of nanometers, making it ideal for this task. Here we introduce two relevant advances: (a) we demonstrate the utility of multi-color super-resolution radial fluctuation light microscopy under cryogenic conditions (cryo-SRRF), and (b) we extend the use of deconvolution processing for dual-axis CSTET data. We show that cryo-SRRF nanoscopy is able to reach resolutions in the range of 100 nm, using commonly available fluorophores and a conventional widefield microscope for cryo-correlative light-electron microscopy. Such resolution aids in precisely identifying regions of interest before tomographic acquisition and enhances precision in localizing features of interest within the 3D reconstruction. Dual-axis CSTET tilt series data and application of entropy regularized deconvolution during post-processing results in close-to-isotropic resolution in the reconstruction without averaging. The integration of cryo-SRRF with deconvolved dual-axis CSTET provides a versatile workflow for studying unique objects in a cell.

Sampling theory perspective on tomographic tilt increment schemes

Given a limited radiation exposure to be distributed over a discrete number of tilted projections in tomography, the optimal collection of information depends on the tilt increment scheme. Relying on principles of sampling theory, several tilt increment schemes can be compared and quantified. Following reasoning of Saxton, a revised scheme is offered in which the tilt angle increments Δθ_n are proportional to 1/cosθ_n. The revised scheme is preferable according to matrix analysis and simulations of geometrical optics. For thin specimens, applying a cosine sampling grid similar to Hoppe's scheme can improve the results. A realistic case is examined by Dr. Probe simulation of a scanning transmission electron microscope (STEM) for an atomic model adapted from the Ferritin protein molecule. Optimal reconstruction methods that are tested include the direct algebraic method, iterative reconstruction, and a new deconvolution-based weighted back-projection, which resembles the correction filter technique in signal recovery from sub-sampled data. A non-linear correction may be accounted for by iteration of the simulation with an ad-hoc atomic model.

Probing Structural Perturbation of Biomolecules by Extracting Cryo-EM Data Heterogeneity

Single-particle cryogenic electron microscopy (cryo-EM) has become an indispensable tool to probe high-resolution structural detail of biomolecules. It enables direct visualization of the biomolecules and opens a possibility for averaging molecular images to reconstruct a three-dimensional Coulomb potential density map. Newly developed algorithms for data analysis allow for the extraction of structural heterogeneity from a massive and low signal-to-noise-ratio (SNR) cryo-EM dataset, expanding our understanding of multiple conformational states, or further implications in dynamics, of the target biomolecule. This review provides an overview that briefly describes the workflow of single-particle cryo-EM, including imaging and data processing, and new methods developed for analyzing the data heterogeneity to understand the structural variability of biomolecules.

Parakeet: a digital twin software pipeline to assess the impact of experimental parameters on tomographic reconstructions for cryo-electron tomography

In cryo-electron tomography (cryo-ET) of biological samples, the quality of tomographic reconstructions can vary depending on the transmission electron microscope (TEM) instrument and data acquisition parameters. In this paper, we present Parakeet, a 'digital twin' software pipeline for the assessment of the impact of various TEM experiment parameters on the quality of three-dimensional tomographic reconstructions. The Parakeet digital twin is a digital model that can be used to optimize the performance and utilization of a physical instrument to enable in silico optimization of sample geometries, data acquisition schemes and instrument parameters. The digital twin performs virtual sample generation, TEM image simulation, and tilt series reconstruction and analysis within a convenient software framework. As well as being able to produce physically realistic simulated cryo-ET datasets to aid the development of tomographic reconstruction and subtomogram averaging programs, Parakeet aims to enable convenient assessment of the effects of different microscope parameters and data acquisition parameters on reconstruction quality. To illustrate the use of the software, we present the example of a quantitative analysis of missing wedge artefacts on simulated planar and cylindrical biological samples and discuss how data collection parameters can be modified for cylindrical samples where a full 180° tilt range might be measured.

A measure for the identification of preferred particle orientations in cryo-electron microscopy data: A simulation study

Cryo-electron microscopy (cryo-EM) is an important experimental technique for the structural analysis of biomolecules that are difficult or impossible to crystallize. The three-dimensional structure of a biomolecule can be reconstructed using two-dimensional electron-density maps, which are experimentally sampled via the electron beam irradiation of vitreous ice in which the target biomolecules are embedded. One assumption required for this reconstruction is that the orientation of the biomolecules in the vitreous ice is isotropic. However, this is not always the case and two-dimensional electron-density maps are often sampled using preferred biomolecular orientations, which can make reconstruction difficult or impossible. Compensation for under-represented views is computationally feasible for the reconstruction of three-dimensional electron density maps, but one must know whether or not there is any missing information in the sampled two-dimensional electron density maps. Thus, a measure to identify whether a cryo-EM data is obtained from the bio­molecules adopting preferred orientations is required. In the present study, we propose a measure for which the geometry of manifold projected onto a low-dimensional space is used. To show the usefulness of the measure, we perform simulations for cryo-EM experiment of a protein. It is found that the geometry of manifold projected onto a two-dimensional space for a protein adopting a preferred biomolecular orientation is significantly different from that for a protein adopting a uniform orientation. This result suggests that the geometry of manifold projected onto a low-dimensional space can be used for the measure for the identification that the biomolecules adopt preferred orientations.

Exploiting prior knowledge about biological macromolecules in cryo-EM structure determination

Three-dimensional reconstruction of the electron-scattering potential of biological macromolecules from electron cryo-microscopy (cryo-EM) projection images is an ill-posed problem. The most popular cryo-EM software solutions to date rely on a regularization approach that is based on the prior assumption that the scattering potential varies smoothly over three-dimensional space. Although this approach has been hugely successful in recent years, the amount of prior knowledge that it exploits compares unfavorably with the knowledge about biological structures that has been accumulated over decades of research in structural biology. Here, a regularization framework for cryo-EM structure determination is presented that exploits prior knowledge about biological structures through a convolutional neural network that is trained on known macromolecular structures. This neural network is inserted into the iterative cryo-EM structure-determination process through an approach that is inspired by regularization by denoising. It is shown that the new regularization approach yields better reconstructions than the current state of the art for simulated data, and options to extend this work for application to experimental cryo-EM data are discussed.

Adeno-Associated Virus (AAV-DJ)-Cryo-EM Structure at 1.56 Å Resolution

Adeno-associated virus is the leading viral vector for gene therapy. AAV-DJ is a recombinant variant developed for tropism to the liver. The AAV-DJ structure has been determined to 1.56 Å resolution through cryo-electron microscopy (cryo-EM). Only apoferritin is reported in preprints at 1.6 Å or higher resolution, and AAV-DJ nearly matches the highest resolutions ever attained through X-ray diffraction of virus crystals. However, cryo-EM has the advantage that most of the hydrogens are clear, improving the accuracy of atomic refinement, and removing ambiguity in hydrogen bond identification. Outside of secondary structures where hydrogen bonding was predictable a priori, the networks of hydrogen bonds coming from direct observation of hydrogens and acceptor atoms are quite different from those inferred even at 2.8 Å resolution. The implications for understanding viral assembly mean that cryo-EM will likely become the favored approach for high resolution structural virology.

Three-dimensional deconvolution processing for STEM cryotomography

The complex environment of biological cells and tissues has motivated development of three-dimensional (3D) imaging in both light and electron microscopies. To this end, one of the primary tools in fluorescence microscopy is that of computational deconvolution. Wide-field fluorescence images are often corrupted by haze due to out-of-focus light, i.e., to cross-talk between different object planes as represented in the 3D image. Using prior understanding of the image formation mechanism, it is possible to suppress the cross-talk and reassign the unfocused light to its proper source post facto. Electron tomography based on tilted projections also exhibits a cross-talk between distant planes due to the discrete angular sampling and limited tilt range. By use of a suitably synthesized 3D point spread function, we show here that deconvolution leads to similar improvements in volume data reconstructed from cryoscanning transmission electron tomography (CSTET), namely a dramatic in-plane noise reduction and improved representation of features in the axial dimension. Contrast enhancement is demonstrated first with colloidal gold particles and then in representative cryotomograms of intact cells. Deconvolution of CSTET data collected from the periphery of an intact nucleus revealed partially condensed, extended structures in interphase chromatin.

Density modification of cryo-EM maps

Density modification uses expectations about features of a map such as a flat solvent and expected distributions of density in the region of the macromolecule to improve individual Fourier terms representing the map. This process transfers information from one part of a map to another and can improve the accuracy of a map. Here, the assumptions behind density modification for maps from electron cryomicroscopy are examined and a procedure is presented that allows the incorporation of model-based information. Density modification works best in cases where unfiltered, unmasked maps with clear boundaries between the macromolecule and solvent are visible, and where there is substantial noise in the map, both in the region of the macromolecule and the solvent. It also is most effective if the characteristics of the map are relatively constant within regions of the macromolecule and the solvent. Model-based information can be used to improve density modification, but model bias can in principle occur. Here, model bias is reduced by using ensemble models that allow an estimation of model uncertainty. A test of model bias is presented that suggests that even if the expected density in a region of a map is specified incorrectly by using an incorrect model, the incorrect expectations do not strongly affect the final map.

LoTToR: An Algorithm for Missing-Wedge Correction of the Low-Tilt Tomographic 3D Reconstruction of a Single-Molecule Structure

A single-molecule three-dimensional (3D) structure is essential for understanding the thermal vibrations and dynamics as well as the conformational changes during the chemical reaction of macromolecules. Individual-particle electron tomography (IPET) is an approach for obtaining a snap-shot 3D structure of an individual macromolecule particle by aligning the tilt series of electron tomographic (ET) images of a targeted particle through a focused iterative 3D reconstruction method. The method can reduce the influence on the 3D reconstruction from large-scale image distortion and deformation. Due to the mechanical tilt limitation, 3D reconstruction often contains missing-wedge artifacts, presented as elongation and an anisotropic resolution. Here, we report a post-processing method to correct the missing-wedge artifact. This low-tilt tomographic reconstruction (LoTToR) method contains a model-free iteration process under a set of constraints in real and reciprocal spaces. A proof of concept is conducted by using the LoTToR on a phantom, i.e., a simulated 3D reconstruction from a low-tilt series of images, including that within a tilt range of ±15°. The method is validated by using both negative-staining (NS) and cryo-electron tomography (cryo-ET) experimental data. A significantly reduced missing-wedge artifact verifies the capability of LoTToR, suggesting a new tool to support the future study of macromolecular dynamics, fluctuation and chemical activity from the viewpoint of single-molecule 3D structure determination.

Development of imaging scaffolds for cryo-electron microscopy

Following recent hardware and software developments, single particle cryo-electron microscopy (cryo-EM) has become one of the most popular structural biology tools. Many targets, such as viruses, large protein complexes and oligomeric membrane proteins, have been resolved to atomic resolution using single-particle cryo-EM, which relies on the accurate assignment of particle location and orientation from intrinsically noisy projection images. The same image processing procedures are more challenging for smaller proteins due to their lower signal-to-noise ratios. Consequently, though most cellular proteins are less than 50kDa, so far it has been possible to solve cryo-EM structures near that size range for only a few favorable cases. Here we highlight some of the challenges and recent efforts to break through this lower size limit by engineering large scaffolds to rigidly display multiple small proteins for imaging. Future design efforts are noted.

Single-Particle Cryo-EM of Membrane Proteins in Lipid Nanodiscs

Single-particle cryo-electron microscopy has become an indispensable technique in structural biology. In particular when studying membrane proteins, it allows the use of membrane-mimicking tools, which can be crucial for a comprehensive understanding of the structure-function relationship of the protein in its native environment. In this chapter we focus on the application of nanodiscs and use our recent studies on the TMEM16 family as an example.

Three-Dimensional High-Energy Electron Radiography Method for Static Mesoscale Samples Diagnostics

In this paper, we propose a new method for static mesoscale sample diagnosis using three-dimensional radiography with high-energy electron radiography (HEER). The principle of three-dimensional high-energy electron radiography (TDHEER) is elucidated, and the feasibility of this method is confirmed by start-to-end simulation results. TDHEER is realized by combining HEER with the three-dimensional reconstruction method, by which more information about the samples can be attained, especially regarding the samples’ internal structures. With our study, the internal structures and the three-dimensional positions of the spherical sample are determined with a ~3 μm resolution. We believe that this new method enhances the HEER diagnostic capability and extends its application potential in mesoscale sciences.

Software for automated acquisition of electron tomography tilt series

For automated acquisition of tilt series for electron tomography, software needs to handle complications such as movements of the sample in x/y and z, increased projected thickness at high tilt, specimen drift, etc. In addition, many applications require special functionality such as low dose acquisition, automated sequential (batch) tomography, or montage tomography. After reviewing how these difficulties can be addressed and a closer look at what advanced acquisition strategies are employed in biosciences, this chapter introduces acquisition software both developed in academia as well as by hardware vendors. It covers the hardware requirements and compatibility, the functional principle and workflow implemented, as well as what advanced functions are supported by the individual programs.

Structural nanotechnology: three-dimensional cryo-EM and its use in the development of nanoplatforms for in vitro catalysis

The organization of enzymes into different subcellular compartments is essential for correct cell function. Protein-based cages are a relatively recently discovered subclass of structurally dynamic cellular compartments that can be mimicked in the laboratory to encapsulate enzymes. These synthetic structures can then be used to improve our understanding of natural protein-based cages, or as nanoreactors in industrial catalysis, metabolic engineering, and medicine. Since the function of natural protein-based cages is related to their three-dimensional structure, it is important to determine this at the highest possible resolution if viable nanoreactors are to be engineered. Cryo-electron microscopy (cryo-EM) is ideal for undertaking such analyses within a feasible time frame and at near-native conditions. This review describes how three-dimensional cryo-EM is used in this field and discusses its advantages. An overview is also given of the nanoreactors produced so far, their structure, function, and applications.

Thresholding of cryo-EM density maps by false discovery rate control

Cryo-EM now commonly generates close-to-atomic resolution as well as intermediate resolution maps from macromolecules observed in isolation and in situ. Interpreting these maps remains a challenging task owing to poor signal in the highest resolution shells and the necessity to select a threshold for density analysis. In order to facilitate this process, a statistical framework for the generation of confidence maps by multiple hypothesis testing and false discovery rate (FDR) control has been developed. In this way, three-dimensional confidence maps contain signal separated from background noise in the form of local detection rates of EM density values. It is demonstrated that confidence maps and FDR-based thresholding can be used for the interpretation of near-atomic resolution single-particle structures as well as lower resolution maps determined by subtomogram averaging. Confidence maps represent a conservative way of interpreting molecular structures owing to minimized noise. At the same time they provide a detection error with respect to background noise, which is associated with the density and is particularly beneficial for the interpretation of weaker cryo-EM densities in cases of conformational flexibility and lower occupancy of bound molecules and ions in the structure.

FIB-SEM imaging properties of Drosophila melanogaster tissues embedded in Lowicryl HM20

Lowicryl resins enable processing of biological material for electron microscopy at the lowest temperatures compatible with resin embedding. When combined with high-pressure freezing and freeze-substitution, Lowicryl embedding supports preservation of fine structural details and fluorescent markers. Here, we analysed the applicability of Lowicryl HM20 embedding for focused ion beam (FIB) scanning electron microscopy (SEM) tomography of Drosophila melanogaster embryonic and larval model systems. We show that the freeze-substitution with per-mill concentrations of uranyl acetate provided sufficient contrast and an image quality of SEM imaging in the range of similar samples analysed by transmission electron microscopy (TEM). Preservation of genetically encoded fluorescent proteins allowed correlative localization of regions of interest (ROI) within the embedded tissue block. TEM on sections cut from the block face enabled evaluation of structural preservation to allow ROI ranking and thus targeted, time-efficient FIB-SEM tomography data collection. The versatility of Lowicryl embedding opens new perspectives for designing hybrid SEM-TEM workflows to comprehensively analyse biological structures. LAY DESCRIPTION: Focused ion beam scanning electron microscopy is becoming a widely used technique for the three-dimensional analysis of biological samples at fine structural details beyond levels feasible for light microscopy. To withstand the abrasion of material by the ion beam and the imaging by the scanning electron beam, biological samples have to be embedded into resins, most commonly these are very dense epoxy-based plastics. However, dense resins generate electron scattering which interferes with the signal from the biological specimen. Furthermore, to improve the imaging contrast, epoxy embedding requires chemical treatments with e.g. heavy metals, which deteriorate the ultrastructure of the biological specimen. In this study we explored the applicability of an electron lucent resin, Lowicryl HM 20, for focused ion beam scanning electron microscopy. The Lowicryl embedding workflow operates at milder chemical treatments and lower temperatures, thus preserving the sub-cellular and sub-organellar organization, as well as fluorescent markers visible by light microscopy. Here we show that focus ion beam scanning electron microscopy of Lowicryl-embedded fruit flies tissues provides reliable imaging revealing fine structural details. Our workflow benefited from use of transmission electron microscopy for the quality control of the ultrastructural preservation and fluorescent light microscopy for localization of regions of interest. The versatility of Lowicryl embedding opens up new perspectives for designing hybrid workflows combining fluorescent light, scanning, and transmission electron microscopy techniques to comprehensively analyze biological structures.

Optimization of Three-Dimensional (3D) Chemical Imaging by Soft X-Ray Spectro-Tomography Using a Compressed Sensing Algorithm

Soft X-ray spectro-tomography provides three-dimensional (3D) chemical mapping based on natural X-ray absorption properties. Since radiation damage is intrinsic to X-ray absorption, it is important to find ways to maximize signal within a given dose. For tomography, using the smallest number of tilt series images that gives a faithful reconstruction is one such method. Compressed sensing (CS) methods have relatively recently been applied to tomographic reconstruction algorithms, providing faithful 3D reconstructions with a much smaller number of projection images than when conventional reconstruction methods are used. Here, CS is applied in the context of scanning transmission X-ray microscopy tomography. Reconstructions by weighted back-projection, the simultaneous iterative reconstruction technique, and CS are compared. The effects of varying tilt angle increment and angular range for the tomographic reconstructions are examined. Optimization of the regularization parameter in the CS reconstruction is explored and discussed. The comparisons show that CS can provide improved reconstruction fidelity relative to weighted back-projection and simultaneous iterative reconstruction techniques, with increasingly pronounced advantages as the angular sampling is reduced. In particular, missing wedge artifacts are significantly reduced and there is enhanced recovery of sharp edges. Examples of using CS for low-dose scanning transmission X-ray microscopy spectroscopic tomography are presented.

The advent of structural biology in situ by single particle cryo-electron tomography

Single particle tomography (SPT), also known as subtomogram averaging, is a powerful technique uniquely poised to address questions in structural biology that are not amenable to more traditional approaches like X-ray crystallography, nuclear magnetic resonance, and conventional cryoEM single particle analysis. Owing to its potential for in situ structural biology at subnanometer resolution, SPT has been gaining enormous momentum in the last five years and is becoming a prominent, widely used technique. This method can be applied to unambiguously determine the structures of macromolecular complexes that exhibit compositional and conformational heterogeneity, both in vitro and in situ. Here we review the development of SPT, highlighting its applications and identifying areas of ongoing development.

The nature and implications of uniformity in the hierarchical organization of nanomaterials

In this Perspective, we present a framework that defines how to understand and control material structure across length scales with inorganic nanoparticles. Three length scales, frequently discussed separately, are unified under the topic of hierarchical organization: atoms arranged into crystalline nanoparticles, ligands arranged on nanoparticle surfaces, and nanoparticles arranged into crystalline superlattices. Through this lens, we outline one potential pathway toward perfect colloidal matter that emphasizes the concept of uniformity. Uniformity is of both practical and functional importance, necessary to increase structural sophistication and realize the promise of nanostructured materials. Thus, we define the nature of nonuniformity at each length scale as a means to guide ongoing research efforts and highlight potential problems in the field.

Correlative Light Electron Microscopy: Connecting Synaptic Structure and Function

Many core paradigms of contemporary neuroscience are based on information obtained by electron or light microscopy. Intriguingly, these two imaging techniques are often viewed as complementary, yet separate entities. Recent technological advancements in microscopy techniques, labeling tools, and fixation or preparation procedures have fueled the development of a series of hybrid approaches that allow correlating functional fluorescence microscopy data and ultrastructural information from electron micrographs from a singular biological event. As correlative light electron microscopy (CLEM) approaches become increasingly accessible, long-standing neurobiological questions regarding structure-function relation are being revisited. In this review, we will survey what developments in electron and light microscopy have spurred the advent of correlative approaches, highlight the most relevant CLEM techniques that are currently available, and discuss its potential and limitations with respect to neuronal and synapse-specific applications.

Adaptive multiresolution method for MAP reconstruction in electron tomography

3D image reconstruction with electron tomography holds problems due to the severely limited range of projection angles and low signal to noise ratio of the acquired projection images. The maximum a posteriori (MAP) reconstruction methods have been successful in compensating for the missing information and suppressing noise with their intrinsic regularization techniques. There are two major problems in MAP reconstruction methods: (1) selection of the regularization parameter that controls the balance between the data fidelity and the prior information, and (2) long computation time. One aim of this study is to provide an adaptive solution to the regularization parameter selection problem without having additional knowledge about the imaging environment and the sample. The other aim is to realize the reconstruction using sequences of resolution levels to shorten the computation time. The reconstructions were analyzed in terms of accuracy and computational efficiency using a simulated biological phantom and publically available experimental datasets of electron tomography. The numerical and visual evaluations of the experiments show that the adaptive multiresolution method can provide more accurate results than the weighted back projection (WBP), simultaneous iterative reconstruction technique (SIRT), and sequential MAP expectation maximization (sMAPEM) method. The method is superior to sMAPEM also in terms of computation time and usability since it can reconstruct 3D images significantly faster without requiring any parameter to be set by the user.

Processing of Structurally Heterogeneous Cryo-EM Data in RELION

This chapter describes algorithmic advances in the RELION software, and how these are used in high-resolution cryo-electron microscopy (cryo-EM) structure determination. Since the presence of projections of different three-dimensional structures in the dataset probably represents the biggest challenge in cryo-EM data processing, special emphasis is placed on how to deal with structurally heterogeneous datasets. As such, this chapter aims to be of practical help to those who wish to use RELION in their cryo-EM structure determination efforts.

Principles of cryo-EM single-particle image processing

Single-particle reconstruction is the process by which 3D density maps are obtained from a set of low-dose cryo-EM images of individual macromolecules. This review considers the fundamental principles of this process and the steps in the overall workflow for single-particle image processing. Also considered are the limits that image signal-to-noise ratio places on resolution and the distinguishing of heterogeneous particle populations.

Single-particle cryo-electron microscopy of macromolecular complexes

Recent technological breakthroughs in image acquisition have enabled single-particle cryo-electron microscopy (cryo-EM) to achieve near-atomic resolution structural information for biological complexes. The improvements in image quality coupled with powerful computational methods for sorting distinct particle populations now also allow the determination of compositional and conformational ensembles, thereby providing key insights into macromolecular function. However, the inherent instability and dynamic nature of biological assemblies remain a tremendous challenge that often requires tailored approaches for successful implementation of the methodology. Here, we briefly describe the fundamentals of single-particle cryo-EM with an emphasis on covering the breadth of techniques and approaches, including low- and high-resolution methods, aiming to illustrate specific steps that are crucial for obtaining structural information by this method.

Electron Tomography: A Three-Dimensional Analytic Tool for Hard and Soft Materials Research

Three-dimensional (3D) structural analysis is essential to understand the relationship between the structure and function of an object. Many analytical techniques, such as X-ray diffraction, neutron spectroscopy, and electron microscopy imaging, are used to provide structural information. Transmission electron microscopy (TEM), one of the most popular analytic tools, has been widely used for structural analysis in both physical and biological sciences for many decades, in which 3D objects are projected into two-dimensional (2D) images. In many cases, 2D-projection images are insufficient to understand the relationship between the 3D structure and the function of nanoscale objects. Electron tomography (ET) is a technique that retrieves 3D structural information from a tilt series of 2D projections, and is gradually becoming a mature technology with sub-nanometer resolution. Distinct methods to overcome sample-based limitations have been separately developed in both physical and biological science, although they share some basic concepts of ET. This review discusses the common basis for 3D characterization, and specifies difficulties and solutions regarding both hard and soft materials research. It is hoped that novel solutions based on current state-of-the-art techniques for advanced applications in hybrid matter systems can be motivated.

A Bayesian approach for suppression of limited angular sampling artifacts in single particle 3D reconstruction

In the single particle reconstruction, the initial 3D structure often suffers from the limited angular sampling artifact. Selecting 2D class averages of particle images generally improves the accuracy and efficiency of the reference-free 3D angle estimation, but causes an insufficient angular sampling to fill the information of the target object in the 3D frequency space. Similarly, the initial 3D structure by the random-conical tilt reconstruction has the well-known "missing cone" artifact. Here, we attempted to solve the limited angular sampling problem by sequentially applying maximum a posteriori estimate with expectation maximization algorithm (sMAP-EM). Using both simulated and experimental cryo-electron microscope images, the sMAP-EM was compared to the direct Fourier method on the basis of reconstruction error and resolution. To establish selection criteria of the final regularization weight for the sMAP-EM, the effects of noise level and sampling sparseness on the reconstructions were examined with evenly distributed sampling simulations. The frequency information filled in the missing cone of the conical tilt sampling simulations was assessed by developing new quantitative measurements. All the results of visual and numerical evaluations showed the sMAP-EM performed better than the direct Fourier method, regardless of the sampling method, noise level, and sampling sparseness. Furthermore, the frequency domain analysis demonstrated that the sMAP-EM can fill the meaningful information in the unmeasured angular space without detailed a priori knowledge of the objects. The current research demonstrated that the sMAP-EM has a high potential to facilitate the determination of 3D protein structures at near atomic-resolution.

A primer to single-particle cryo-electron microscopy

Cryo-electron microscopy (cryo-EM) of single-particle specimens is used to determine the structure of proteins and macromolecular complexes without the need for crystals. Recent advances in detector technology and software algorithms now allow images of unprecedented quality to be recorded and structures to be determined at near-atomic resolution. However, compared with X-ray crystallography, cryo-EM is a young technique with distinct challenges. This primer explains the different steps and considerations involved in structure determination by single-particle cryo-EM to provide an overview for scientists wishing to understand more about this technique and the interpretation of data obtained with it, as well as a starting guide for new practitioners.

A tilt-pair based method for assigning the projection directions of randomly oriented single-particle molecules

In this article, we describe an improved method to assign the projection angle for averaged images using tilt-pair images for three-dimensional reconstructions from randomly oriented single-particle molecular images. Our study addressed the so-called 'initial volume problem' in the single-particle reconstruction, which involves estimation of projection angles of the particle images. The projected images of the particles in different tilt observations were mixed and averaged for the characteristic views. After the ranking of these group average images in terms of reliable tilt angle information, mutual tilt angles between images are assigned from the constituent tilt-pair information. Then, multiples of the conical tilt series are made and merged to construct a network graph of the particle images in terms of projection angles, which are optimized for the three-dimensional reconstruction. We developed the method with images of a synthetic object and applied it to a single-particle image data set of the purified deacetylase from archaea. With the introduction of low-angle tilt observations to minimize unfavorable imaging conditions due to tilting, the results demonstrated reasonable reconstruction models without imposing symmetry to the structure. This method also guides its users to discriminate particle images of different conformational state of the molecule.

3D image reconstruction of fiber systems using electron tomography

Over the past several years, electron microscopists and materials researchers have shown increased interest in electron tomography (reconstruction of three-dimensional information from a tilt series of bright field images obtained in a transmission electron microscope (TEM)). In this research, electron tomography has been used to reconstruct a three-dimensional image for fiber structures from secondary electron images in a scanning electron microscope (SEM). The implementation of this technique is used to examine the structure of fiber system before and after deformation. A test sample of steel wool was tilted around a single axis from -10° to 60° by one-degree steps with images taken at every degree; three-dimensional images were reconstructed for the specimen of fine steel fibers. This method is capable of reconstructing the three-dimensional morphology of this type of lineal structure, and to obtain features such as tortuosity, contact points, and linear density that are of importance in defining the mechanical properties of these materials.

Compensation of missing wedge effects with sequential statistical reconstruction in electron tomography

Electron tomography (ET) of biological samples is used to study the organization and the structure of the whole cell and subcellular complexes in great detail. However, projections cannot be acquired over full tilt angle range with biological samples in electron microscopy. ET image reconstruction can be considered an ill-posed problem because of this missing information. This results in artifacts, seen as the loss of three-dimensional (3D) resolution in the reconstructed images. The goal of this study was to achieve isotropic resolution with a statistical reconstruction method, sequential maximum a posteriori expectation maximization (sMAP-EM), using no prior morphological knowledge about the specimen. The missing wedge effects on sMAP-EM were examined with a synthetic cell phantom to assess the effects of noise. An experimental dataset of a multivesicular body was evaluated with a number of gold particles. An ellipsoid fitting based method was developed to realize the quantitative measures elongation and contrast in an automated, objective, and reliable way. The method statistically evaluates the sub-volumes containing gold particles randomly located in various parts of the whole volume, thus giving information about the robustness of the volume reconstruction. The quantitative results were also compared with reconstructions made with widely-used weighted backprojection and simultaneous iterative reconstruction technique methods. The results showed that the proposed sMAP-EM method significantly suppresses the effects of the missing information producing isotropic resolution. Furthermore, this method improves the contrast ratio, enhancing the applicability of further automatic and semi-automatic analysis. These improvements in ET reconstruction by sMAP-EM enable analysis of subcellular structures with higher three-dimensional resolution and contrast than conventional methods.

Macromolecular 3D SEM reconstruction strategies: signal to noise ratio and resolution

Three-dimensional scanning electron microscopy generates quantitative volumetric structural data from SEM images of macromolecules. This technique provides a quick and easy way to define the quaternary structure and handedness of protein complexes. Here, we apply a variety of preparation and imaging methods to filamentous actin in order to explore the relationship between resolution, signal-to-noise ratio, structural preservation and dataset size. This information can be used to define successful imaging strategies for different applications.

Towards an integrative structural biology approach: combining Cryo-TEM, X-ray crystallography, and NMR

Cryo-transmission electron microscopy (Cryo-TEM) and particularly single particle analysis is rapidly becoming the premier method for determining the three-dimensional structure of protein complexes, and viruses. In the last several years there have been dramatic technological improvements in Cryo-TEM, such as advancements in automation and use of improved detectors, as well as improved image processing techniques. While Cryo-TEM was once thought of as a low resolution structural technique, the method is currently capable of generating nearly atomic resolution structures on a routine basis. Moreover, the combination of Cryo-TEM and other methods such as X-ray crystallography, nuclear magnetic resonance spectroscopy, and molecular dynamics modeling are allowing researchers to address scientific questions previously thought intractable. Future technological developments are widely believed to further enhance the method and it is not inconceivable that Cryo-TEM could become as routine as X-ray crystallography for protein structure determination.

CTER-rapid estimation of CTF parameters with error assessment

In structural electron microscopy, the accurate estimation of the Contrast Transfer Function (CTF) parameters, particularly defocus and astigmatism, is of utmost importance for both initial evaluation of micrograph quality and for subsequent structure determination. Due to increases in the rate of data collection on modern microscopes equipped with new generation cameras, it is also important that the CTF estimation can be done rapidly and with minimal user intervention. Finally, in order to minimize the necessity for manual screening of the micrographs by a user it is necessary to provide an assessment of the errors of fitted parameters values. In this work we introduce CTER, a CTF parameters estimation method distinguished by its computational efficiency. The efficiency of the method makes it suitable for high-throughput EM data collection, and enables the use of a statistical resampling technique, bootstrap, that yields standard deviations of estimated defocus and astigmatism amplitude and angle, thus facilitating the automation of the process of screening out inferior micrograph data. Furthermore, CTER also outputs the spatial frequency limit imposed by reciprocal space aliasing of the discrete form of the CTF and the finite window size. We demonstrate the efficiency and accuracy of CTER using a data set collected on a 300kV Tecnai Polara (FEI) using the K2 Summit DED camera in super-resolution counting mode. Using CTER we obtained a structure of the 80S ribosome whose large subunit had a resolution of 4.03Å without, and 3.85Å with, inclusion of astigmatism parameters.

Projection-based volume alignment

When heterogeneous samples of macromolecular assemblies are being examined by 3D electron microscopy (3DEM), often multiple reconstructions are obtained. For example, subtomograms of individual particles can be acquired from tomography, or volumes of multiple 2D classes can be obtained by random conical tilt reconstruction. Of these, similar volumes can be averaged to achieve higher resolution. Volume alignment is an essential step before 3D classification and averaging. Here we present a projection-based volume alignment (PBVA) algorithm. We select a set of projections to represent the reference volume and align them to a second volume. Projection alignment is achieved by maximizing the cross-correlation function with respect to rotation and translation parameters. If data are missing, the cross-correlation functions are normalized accordingly. Accurate alignments are obtained by averaging and quadratic interpolation of the cross-correlation maximum. Comparisons of the computation time between PBVA and traditional 3D cross-correlation methods demonstrate that PBVA outperforms the traditional methods. Performance tests were carried out with different signal-to-noise ratios using modeled noise and with different percentages of missing data using a cryo-EM dataset. All tests show that the algorithm is robust and highly accurate. PBVA was applied to align the reconstructions of a subcomplex of the NADH: ubiquinone oxidoreductase (Complex I) from the yeast Yarrowia lipolytica, followed by classification and averaging.

Cryo-electron microscopy--a primer for the non-microscopist

Cryo-electron microscopy (cryo-EM) is increasingly becoming a mainstream technology for studying the architecture of cells, viruses and protein assemblies at molecular resolution. Recent developments in microscope design and imaging hardware, paired with enhanced image processing and automation capabilities, are poised to further advance the effectiveness of cryo-EM methods. These developments promise to increase the speed and extent of automation, and to improve the resolutions that may be achieved, making this technology useful to determine a wide variety of biological structures. Additionally, established modalities for structure determination, such as X-ray crystallography and nuclear magnetic resonance spectroscopy, are being routinely integrated with cryo-EM density maps to achieve atomic-resolution models of complex, dynamic molecular assemblies. In this review, which is directed towards readers who are not experts in cryo-EM methodology, we provide an overview of emerging themes in the application of this technology to investigate diverse questions in biology and medicine. We discuss the ways in which these methods are being used to study structures of macromolecular assemblies that range in size from whole cells to small proteins. Finally, we include a description of how the structural information obtained by cryo-EM is deposited and archived in a publicly accessible database.

Optimal noise reduction in 3D reconstructions of single particles using a volume-normalized filter

The high noise level found in single-particle electron cryo-microscopy (cryo-EM) image data presents a special challenge for three-dimensional (3D) reconstruction of the imaged molecules. The spectral signal-to-noise ratio (SSNR) and related Fourier shell correlation (FSC) functions are commonly used to assess and mitigate the noise-generated error in the reconstruction. Calculation of the SSNR and FSC usually includes the noise in the solvent region surrounding the particle and therefore does not accurately reflect the signal in the particle density itself. Here we show that the SSNR in a reconstructed 3D particle map is linearly proportional to the fractional volume occupied by the particle. Using this relationship, we devise a novel filter (the "single-particle Wiener filter") to minimize the error in a reconstructed particle map, if the particle volume is known. Moreover, we show how to approximate this filter even when the volume of the particle is not known, by optimizing the signal within a representative interior region of the particle. We show that the new filter improves on previously proposed error-reduction schemes, including the conventional Wiener filter as well as figure-of-merit weighting, and quantify the relationship between all of these methods by theoretical analysis as well as numeric evaluation of both simulated and experimentally collected data. The single-particle Wiener filter is applicable across a broad range of existing 3D reconstruction techniques, but is particularly well suited to the Fourier inversion method, leading to an efficient and accurate implementation.

Real-space processing of helical filaments in SPARX

We present a major revision of the iterative helical real-space refinement (IHRSR) procedure and its implementation in the SPARX single particle image processing environment. We built on over a decade of experience with IHRSR helical structure determination and we took advantage of the flexible SPARX infrastructure to arrive at an implementation that offers ease of use, flexibility in designing helical structure determination strategy, and high computational efficiency. We introduced the 3D projection matching code which now is able to work with non-cubic volumes, the geometry better suited for long helical filaments, we enhanced procedures for establishing helical symmetry parameters, and we parallelized the code using distributed memory paradigm. Additional features include a graphical user interface that facilitates entering and editing of parameters controlling the structure determination strategy of the program. In addition, we present a novel approach to detect and evaluate structural heterogeneity due to conformer mixtures that takes advantage of helical structure redundancy.

Cryo-electron tomography for structural characterization of macromolecular complexes

Cryo-electron tomography (cryo-ET) is an emerging 3-D reconstruction technology that combines the principles of tomographic 3-D reconstruction with the unmatched structural preservation of biological matter embedded in vitreous ice. Cryo-ET is particularly suited to investigating cell-biological samples and large macromolecular structures that are too polymorphic to be reconstructed by classical averaging-based 3-D reconstruction procedures. This unit aims to make cryo-ET accessible to newcomers and discusses the specialized equipment required, as well as relevant advantages and hurdles associated with sample preparation by vitrification and cryo-ET. Protocols describe specimen preparation, data recording and 3-D data reconstruction for cryo-ET, with a special focus on macromolecular complexes. A step-by-step procedure for specimen vitrification by plunge freezing is provided, followed by the general practicalities of tilt-series acquisition for cryo-ET, including advice on how to select an area appropriate for acquiring a tilt series. A brief introduction to the underlying computational reconstruction principles applied in tomography is described, along with instructions for reconstructing a tomogram from cryo-tilt series data. Finally, a method is detailed for extracting small subvolumes containing identical macromolecular structures from tomograms for alignment and averaging as a means to increase the signal-to-noise ratio and eliminate missing wedge effects inherent in tomographic reconstructions.